Although these three versions of GR are fully equivalent from a dynamical point of view, the basic principles on which they are formulated are very different. Furthermore, their modifications are not equivalent at all being the theories formulated in different geometries. Hence, one can find a wide range of possibilities and interpretations that have to be consistently compared with observational and experimental data. For example, also if GR and TEGR are dinamically equivalent, this is not the case for \(f(R)\)  gravity [1]}, [2]} and \(f(T)\)  gravity [3]}, [4]}, [5]}, [6]}. The first is a fourth-order theory in metric formulation, the latter remain a second-order theory like GR and TEGR.
